In many situations it is important to find a lost object, person or animal. If a small radio-frequency (RF) transmitter is attached to a dog's leash or to a child's clothes or wrist, for example, the signal can be used to find the missing dog or child.
Known methods are available to determine the direction of arrival (DoA) of an incoming signal, and thereby the direction in which the transmitter can be found, and to determine the distance to the transmitter.
Received power can be used to estimate the distance between the transmitter and receiver. A benefit of methods based on received power is that hardware and signal processing requirements are minimised. However, the received power depends on the transmitted power, antenna gains, and the environment through which the signal propagates. Because of the influence of the environment, the relationship between the received power and the distance between transmitter and receiver is not straightforward, such that it is difficult to obtain an accurate estimate. The distance can be estimated most accurately when there is a line-of-sight (LOS) between the transmitter and receiver. In this case, the average received power decreases approximately relative to the distance squared.
Methods based on received power may involve pathloss, which is related to received power after removing fast fading. (Received power is equal to transmitted power, plus path loss, plus slow fading, plus fast fading. Fast fading can be removed rather easily; slow fading is more difficult.)
A commonly-used model for pathloss (PL) isPL=−10·γ·log10(r)+PL0   (1)where r is the distance between transmitter and receiver, γ is a pathloss exponent, and PL0 is the pathloss at a given distance, for example 1 m.
Utilising this model has some problems caused by propagation distortion. Objects like buildings or walls between the transmitter and receiver attenuate the signal, and this attenuation (shadow fading) does not depend directly on distance.
Other distance-estimation methods use the phase of the received signal or a propagation delay between the transmitter and receiver. However, such methods require very accurate time synchronisation between the transmitter and receiver, which is not feasible with standard hardware. Another distance-estimation method is to have a GPS receiver at each of the transmitter and receiver and a communication method to exchange coordinates.
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